Homoclinic intersections for geodesic flows on convex spheres

Zhihong Xia; Pengfei Zhang

doi:10.1090/conm/698/13980

Homoclinic intersections for geodesic flows on convex spheres

Zhihong Xia, Pengfei Zhang

Mathematics

Research output: Chapter in Book/Report/Conference proceeding › Chapter

2 Scopus citations

Abstract

In this paper, we study some generic properties of the geodesic flows on a convex sphere. We prove that, C^r generically (2 ≤ r ≤ ∞), every hyperbolic closed geodesic on S² admits some transverse homoclinic intersections.

Original language	English (US)
Title of host publication	Contemporary Mathematics
Publisher	American Mathematical Society
Pages	221-238
Number of pages	18
DOIs	https://doi.org/10.1090/conm/698/13980
State	Published - 2017

Publication series

Name	Contemporary Mathematics
Volume	698
ISSN (Print)	0271-4132
ISSN (Electronic)	1098-3627

Funding

This research is supported in part by National Science Foundation. The authors are very grateful to the anonymous referee for many useful comments and suggestions, which helped them to improve the presentation of the paper significantly.

Keywords

Closed geodesic
Convex spheres
Elliptic geodesic
Geodesic flow
Hyperbolic geodesic
Nonlinearly stable
Prime-end compactification
Transverse homoclinic intersections

ASJC Scopus subject areas

General Mathematics

Access to Document

10.1090/conm/698/13980

Cite this

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title = "Homoclinic intersections for geodesic flows on convex spheres",

abstract = "In this paper, we study some generic properties of the geodesic flows on a convex sphere. We prove that, Cr generically (2 ≤ r ≤ ∞), every hyperbolic closed geodesic on S2 admits some transverse homoclinic intersections.",

keywords = "Closed geodesic, Convex spheres, Elliptic geodesic, Geodesic flow, Hyperbolic geodesic, Nonlinearly stable, Prime-end compactification, Transverse homoclinic intersections",

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KW - Elliptic geodesic

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KW - Nonlinearly stable

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KW - Transverse homoclinic intersections

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Homoclinic intersections for geodesic flows on convex spheres

Abstract

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Keywords

ASJC Scopus subject areas

Access to Document

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